What's being presupposed in addition to the polarity
Considering the intent of that particular example, I believe that this sentence is simply explicitly highlighting the trivial, perhaps tautological presupposition to illustrate that even though we might not think about it, such sentences imply the polarity and if we want to be careful, that should be considered. Also, the "storytelling" function of that presupposition example is in contrast with the following two examples of more substantial presuppositions.
However, if we go into detail, I can imagine situations where the true answer to questions in the style of "is there a professor of linguistics at [institution]" is not yes, not no, but "it's complicated", where the exact answer depends on nuances of how you interpret the question. Perhaps at this very moment professors are home and not physically "at" the institution, perhaps they have more specific titles e.g. professor of phonology so they have de facto professors of linguistics without having anyone with the title "professor of linguistics", etc.
So perhaps the main presupposition is that the categories used are well-defined with strict boundaries - that there is some clear unambiguous criteria that can be used to evaluate, for example, if a particular person is "professor of linguistics at MIT". Law of excluded middle is tricky to apply without very formal definitions - in this case we can perhaps dismiss it as trivial, but not in the general case.
For example, consider a somewhat politically loaded question of "Is there a woman in this room?" in the situation where the room contains a transgender person; the question carries an automatic presupposition that the question has a yes/no answer, which implies a presupposition that the categories used (i.e "woman") have a clear boundary and a common definition shared by all participants in the discourse - which isn't always true. So even if a sentence just presupposes polarity, that might be a quite strong presupposition in some cases.